Objectives
The relationship between axioms and definitions has been a key turning point in the contemporary transformation of logic, mathematics and science, following the birth and development of modern axiomatics and the radical changes in the definitions of the fundamental notions of mathematics : number, size, set. It is often said that definitions play no role in axiomatic systems except as abbreviations. Axioms are often considered as implicit definitions or characterizations of the primitive terms that appear in axioms. The project approaches the study of axiomatic definitions from two complementary perspectives : historical and theoretical. Accordingly, the project will have two main objectives, respectively 1) to investigate the origin of the notion of axiomatic definitions, and 2) to classify axiomatic definitions and study the kind of problems they are applied to in logic and philosophy of mathematics. }
Summary table of persons involved in the project :
- Centre Gilles Gaston Granger (CGGG UMR 7304), Université Aix-Marseille and CNRS :
- CANTU Paola - Directrice de recherche CNRS, DR, Coordinatrice scientifique
- CROCCO Gabriella, Professeure des Universités
- BERNARD Julien, Maître de conférences
- DEBUICHE Valérie, Maîtresse de conférences
- Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST UMR), Université Paris 1 and CNRS
- WAGNER Pierre, Professeur des Universités, partenaire scientifique
- PANZA Marco, Directeur de Recherche CNRS
- POGGIOLESI Francesca, Chercheure CNRS CRCN
- ANTONUTTI-MARFORI Marianna, Maîtresse de conférences
- NAIBO Alberto, Maître de conférences
- Sciences, Philosophie, Histoire (SPHERE UMR 7219), Université Paris Cité and CNRS
- DE RISI Vincenzo, Directeur CNRS CRCN, partenaire scientifique
- HALIMI Brice, Professeur des Universités
- CONFALONIERI Sara, Maîtresse de conférences
